morlet wavelet

How Does the Morlet Wavelet Work?

The Morlet wavelet is defined by a complex exponential modulated by a Gaussian function. Mathematically, it can be represented as:
\[ \psi(t) = \pi^{-1/4} e^{i \omega_0 t} e^{-t^2 / 2} \]
where \( \omega_0 \) is the central frequency. The wavelet transform of a time series \( x(t) \) is given by:
\[ W_x(s, \tau) = \int_{-\infty}^{\infty} x(t) \psi^*\left(\frac{t-\tau}{s}\right) dt \]
Here, \( s \) represents the scale (related to frequency), and \( \tau \) represents the time shift. The resulting coefficients \( W_x(s, \tau) \) provide a time-frequency representation of the data.

Frequently asked queries:

Why Use Morlet Wavelet in Epidemiology?
How Does the Morlet Wavelet Work?
What Are the Advantages of Multivalent Vaccines?
What is Mobile Data Collection in Epidemiology?
What is Moderated Mediation?
Why are Prophylactic Measures Important?
What is Case Investigation in Epidemiology?
Why is Infrastructure Important?
What Are the Key Steps in Regulatory Approval?
How is the Bonferroni Correction Applied?
What Measures Can Be Taken to Ensure Data Confidentiality?
What Challenges Exist in Environmental Health Epidemiology?
How Do Search Engine Queries Reflect Disease Trends?
What is the Epidemiology of Osteoporosis?
What Are Some Methods Used in Genetic Epidemiology?
What is a Crossover RCT?
How Do Mobile Applications Aid in Data Collection?
What is Prenatal Care?
How to Optimize Follow-Up Reminders?
What are the Symptoms of TBE?
Follow Us
Top Searches
Andes Virus COVID-19 Patients Field Epidemiology Genetic Diagnosis Genetic Variants Global Health Public Health Education

Partnered Content Networks

Relevant Topics